The Convolution Method
Free SOA Exam FAM (Fundamentals of Actuarial Mathematics) lesson in Severity, Frequency, and Aggregate Models. 9 min read, ~1,335 words.
Discrete convolution:. Convolution yields exact distributions with no approximation, unlike normal or lognormal methods. For more variables: convolve iteratively, first, then add. Collective risk model: condition on, then compute the n-fold convolution for each. Exam strategy: enumerate only the pairs that produce the target sum, not the full distribution. Verification...
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